The invention relates to methods of color sensing and estimation. More particularly the invention relates to techniques for determining RGB filter set and color estimation performance for RGB LED color sensing.
In the field of color sensing it is known that any instrument or process used to distinguish or sense colors as the human eye does must have spectral responses which correspond to some linear transformation of the CIE color mixture functions x(λ), y(λ), z(λ). In color photography this condition is known as the Luther-Ives condition. There are infinitely many real coefficients a1, a2 and a3, such that C(λ)=a1 x(λ)+a2 y(λ)+a3 z(λ), represents an equivalent new color matching function C(λ). All functions of the C(λ) family are equivalent under matrix transformation.
There is much greater freedom when using color filters for color sensing to approximately realize C(λ) for a set of coefficients instead of physically realizing the CIE color matching functions. Since there are infinitely many equivalent C(λ)'s, an appropriate set of C(λ)'s must be determined for a given color filter set.
In order to be approximated by practical color filters, the new transformed color matching functions need to satisfy three conditions: 1) C(λ) is positive or zero throughout the entire spectral range; 2) C(λ) has a single peak; 3) the overlaps between the three C(λ)'s are as small as possible.
One transformation matrix satisfying the above conditions is the well known MacAdam's matrix given by:
      M    ⁢                  ⁢    c    =      (                            0.5115                          0.5985                                      -            0.11                                                            -            0.5081                                    1.4093                          0.0988                                      0                          0                          1                      )  
The MacAdam's matrix satisfies the conditions for color matching functions that may be realized by real filters and is therefore of use in the design of filter sets for specific color sensing applications. Custom designed filters sets are particularly expensive to implement, especially when the filter must be designed in a specialized shape. For many applications of color sensing, the custom designed filters necessary for optimal estimation are too expensive. It would be desirable to provide a method of utilizing existing low cost filters for sub-optimal color sensing to overcome these and other limitations.